Optimization of Circuits for IBM's five-qubit Quantum Computers

IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement gates from the Clifford+T gate library. However, each architecture only implements a subset of the possible CNOT gates. In this paper, we show how Clifford+T circuits can efficiently be mapped into the two IBM quantum computers with 5 qubits. We further present an algorithm and a set of circuit identities that may be used to optimize the Clifford+T circuits in terms of gate count and number of levels. It is further shown that the optimized circuits can considerably reduce the gate count and number of levels and thus produce results with better fidelity

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

A Hierarchical Approach to Computer-Aided Design of Quantum Circuits

A new approach to synthesis of permutation class of quantum logic circuits has been proposed in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). First we synthesize a library of permutation (pseudobinary) gates using a Computer-Aided-Design approach that links evolutionary and combinatorics approaches with human experience and creativity. Next the circuit is designed using these gates and standard 1*1 and 2*2 quantum gates and finally the optimizing tautological transforms are applied to the circuit, producing a sequence of quantum operations being close to operations practically realizable. These hierarchical stages can be compared to standard gate library design, generic logic synthesis and technology mapping stages of classical CAD systems, respectively. We use an informed genetic algorithm to evolve arbitrary quantum circuit specified by a (target) unitary matrix, specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes, and an evolutionary algorithm specialized to permutation circuits specified by truth tables. We outline interactive CAD approach in which the designer is a part of feedback loop in evolutionary program and the search is not for circuits of known specifications, but for any gates with high processing power and small cost for given constraints. In contrast to previous approaches, our methodology allows synthesis of both: small quantum circuits of arbitrary type (gates), and permutation class circuits that are well realizable in particular technology